I use the concept of absolute value when helping students add unlike signed numbers as the rule I use is Take the sign of the largest number (you have to think absolute value or otherwise it would always be the positive number) and find the difference.

Greatest Common Factor = Low number for reducing fractions
Lowest Common Denominator High number for adding or subtracting fractions with different denominators

e.g 3 and 8 or (2.2.2) In this case there is no reduction possible so the GCF is 1
3 and 8 for LCD 3 and 2.2.2. Since there are no common factors, multiply all =24

Question: Now what is all this Absolute Number business all about, which in itself I do get, but then we get such things as -(-8) which = 8 is read as "the opposite of negative 8." I get that in an abstract sense, but processing that to bring it to a level of automaticity is another thing altogether.

More importantly,

* What is the significance of this level of mastery when students are working on basic integers?
* What is its actual mathematical function?
* Intuitively, I'm sensing that it may have some value when it comes to algebra (yes? no?) and if so then perhaps higher levels of absolute number functionality can be taught at that time (yes? no?) after students mastered more of the basics of negative numbers, fractions, decimals, proportions and basic algebraic equations

This brings up to my mind the importance of:

1. Sequencing skill development from basic to more advanced
2. Maximum possible simplicity as a critical scaffolding strategy in its own right
3. Incorporating mathematical meaning making and inquiry as a critical part of the ongoing work
4. Individual and collaborative scaffolding

BTW I think these and other pivotal steps have more overall pedagogical significance than say whether or not or the extent to which one utilizes manipulatives. To be sure manipulatives and other methods can be important, but I would view such methods as a secondary rather than a primary issue. In short, they belong in the arsenal of teaching tools in the facilitation of the primary goal--learning.

Best,

George Demetrion

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Date: Mon, 8 Feb 2010 16:18:30 -0700
Subject: Re: [Numeracy 109] introductions
From: dickins2 at wncc.netTo: gdemetrion at msn.com; numeracy at nifl.govWhat is the difference between the Lowest (or least) Common Denominator and the Least Common Multiple and what different functions do they accomplish?

The LCD is the smallest number that will go INTO each of the numbers, while the LCM is the smallest number that each of the numbers will divide into (the smallest number that is a multiple of both numbers).

Suppose the numbers are 15 and 21. The LCD would be 3: 15 = 3 * 5; 21 = 3 * 7. The number they have *in common* is 3.
Suppose the numbers are 49 and 98. The LCD would be 49: 49 = 7 * 7; 98 = 7 * 7 * 2. The numbers they have *in common* are 7 and 7, and 7 * 7 = 49.

Try 45 and 21 for the LCM. What is the smallest number that is a multiple of both numbers? 45 = 3 * 3 * 5, 21 = 3 * 7. The LCM = 3 * 3 * 5 * 7 or 105. (Each number has a 3, so the first three only counts once. There is an extra 3 in 45, plus the 5. 21 still has a 7. Multiply all those together.
Or let's try 15 and 49. 15 = 3 * 5, 49 = 7 * 7. No numbers in common, so multiply them all together. LCM = 3 * 5 * 7 * 7 or 735.

While I am an experienced adult educator I am a newbie math teacher, but I'm plugging away in my first transitions to college basic math course.

We've had two three hour sessions thus far in a 15 week course and things are moving along okay.

To be sure I've put a lot of time practicing my math through basic algebra and concentrating on the assignments in our weekly sessions.

I'm learning and I'm also getting a good experiential dose of math phobia, which in turn, in the process of transforming in the process of learning and then drawing on my overall teaching skills, especially incorporating basic explanation, a lot of practice and collaborative scaffolding instructional processes.

One technical question:

What is the difference between the Lowest (or least) Common Denominator and the Least Common Multiple and what different functions do they accomplish?

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